Problem: Simplify the following expression: $\dfrac{18k^5}{20k}$ You can assume $k \neq 0$.
Answer: $ \dfrac{18k^5}{20k} = \dfrac{18}{20} \cdot \dfrac{k^5}{k} $ To simplify $\frac{18}{20}$ , find the greatest common factor (GCD) of $18$ and $20$ $18 = 2 \cdot 3 \cdot 3$ $20 = 2 \cdot 2 \cdot 5$ $ \mbox{GCD}(18, 20) = 2 $ $ \dfrac{18}{20} \cdot \dfrac{k^5}{k} = \dfrac{2 \cdot 9}{2 \cdot 10} \cdot \dfrac{k^5}{k} $ $\phantom{ \dfrac{18}{20} \cdot \dfrac{5}{1}} = \dfrac{9}{10} \cdot \dfrac{k^5}{k} $ $ \dfrac{k^5}{k} = \dfrac{k \cdot k \cdot k \cdot k \cdot k}{k} = k^4 $ $ \dfrac{9}{10} \cdot k^4 = \dfrac{9k^4}{10} $